matrix analysis for statistics 3rd edition

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Matrix Analysis For Statistics

Author : James R. Schott
ISBN : 9781119092469
Genre : Mathematics
File Size : 48. 4 MB
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An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.

Linear Algebra And Matrix Analysis For Statistics

Author : Sudipto Banerjee
ISBN : 9781420095388
Genre : Mathematics
File Size : 31. 64 MB
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Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.

Multivariate Statistical Methods

Author : Bryan F.J. Manly
ISBN : 1584884142
Genre : Mathematics
File Size : 72. 86 MB
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Multivariate methods are now widely used in the quantitative sciences as well as in statistics because of the ready availability of computer packages for performing the calculations. While access to suitable computer software is essential to using multivariate methods, using the software still requires a working knowledge of these methods and how they can be used. Multivariate Statistical Methods: A Primer, Third Edition introduces these methods and provides a general overview of the techniques without overwhelming you with comprehensive details. This thoroughly revised, updated edition of a best-selling introductory text retains the author's trademark clear, concise style but includes a range of new material, new exercises, and supporting materials on the Web. New in the Third Edition: Fully updated references Additional examples and exercises from the social and environmental sciences A comparison of the various statistical software packages, including Stata, Statistica, SAS Minitab, and Genstat, particularly in terms of their ease of use by beginners In his efforts to produce a book that is as short as possible and that enables you to begin to use multivariate methods in an intelligent manner, the author has produced a succinct and handy reference. With updated information on multivariate analyses, new examples using the latest software, and updated references, this book provides a timely introduction to useful tools for statistical analysis.

Statistical Methods For Trend Detection And Analysis In The Environmental Sciences

Author : Richard Chandler
ISBN : 9781119991960
Genre : Mathematics
File Size : 77. 7 MB
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The need to understand and quantify change is fundamental throughout the environmental sciences. This might involve describing past variation, understanding the mechanisms underlying observed changes, making projections of possible future change, or monitoring the effect of intervening in some environmental system. This book provides an overview of modern statistical techniques that may be relevant in problems of this nature. Practitioners studying environmental change will be familiar with many classical statistical procedures for the detection and estimation of trends. However, the ever increasing capacity to collect and process vast amounts of environmental information has led to growing awareness that such procedures are limited in the insights that they can deliver. At the same time, significant developments in statistical methodology have often been widely dispersed in the statistical literature and have therefore received limited exposure in the environmental science community. This book aims to provide a thorough but accessible review of these developments. It is split into two parts: the first provides an introduction to this area and the second part presents a collection of case studies illustrating the practical application of modern statistical approaches to the analysis of trends in real studies. Key Features: Presents a thorough introduction to the practical application and methodology of trend analysis in environmental science. Explores non-parametric estimation and testing as well as parametric techniques. Methods are illustrated using case studies from a variety of environmental application areas. Looks at trends in all aspects of a process including mean, percentiles and extremes. Supported by an accompanying website featuring datasets and R code. The book is designed to be accessible to readers with some basic statistical training, but also contains sufficient detail to serve as a reference for practising statisticians. It will therefore be of use to postgraduate students and researchers both in the environmental sciences and in statistics.

Introduction To Bayesian Statistics

Author : William M. Bolstad
ISBN : 9781118593226
Genre : Mathematics
File Size : 50. 2 MB
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"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods." There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features: Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods Exercises throughout the book that have been updated to reflect new applications and the latest software applications Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics.

Matrix Computations

Author : Gene H. Golub
ISBN : 0801854148
Genre : Mathematics
File Size : 26. 69 MB
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"An invaluable reference book that should be in every university library." -- Image: Bulletin of the International Linear Algebra Society

Matrix Differential Calculus With Applications In Statistics And Econometrics

Author : Jan R. Magnus
ISBN : 047198633X
Genre : Mathematics
File Size : 84. 75 MB
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This text is a self-contained and unified treatment of matrix differential calculus, specifically written for econometricians and statisticians. It can serve as a textbook for advanced undergraduates and postgraduates in econometrics and as a reference book for practising econometricians.

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